JP2015032885A - Coding apparatus and decoding apparatus - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a coding apparatus and a decoding apparatus capable of achieving high performance without requiring high arithmetic capacity while suppressing memory capacity to low capacity.SOLUTION: An erasure correction coding part 12, when transmitting error correction code sequences obtained by respectively coding a plurality of information sequences, performs coding of other error correction codes including partial data of a certain error correction code sequence. An erasure correction decoding part 22 decodes the error correction code sequence received first, and when the decoding succeeds, performs decoding of the succeeding error correction code while leaving only data related to other error correction codes. When the decoding fails, the erasure correction decoding part 22 decodes the succeeding error correction code while leaving data related to other error correction codes and succeeding in decoding, calculation intermediate value data and information on a position failing in decoding, and then performs decoding by a similar procedure.

Description

  The present invention relates to an encoding apparatus that encodes an error correction code for correcting a transmission error that occurs on a transmission path, and a decoding apparatus that decodes the same.

  In general erasure correction encoding / decoding, for example, the erasure correction code is used for encoding in units of packets on the transmitter side, and the receiver side receives a packet sequence partially lost by the communication path, Based on the successfully received packet, the lost packet is decoded by Gaussian elimination or the like. Note that a lost packet is a packet that has failed to be received, and a packet that has failed to be received is expressed as lost because information on all the bits constituting the packet cannot be obtained. As such a conventional decoding method, there has been one as shown in Non-Patent Document 1, for example.

Murotsu, Wadayama, Yamakita, "Erasure Error Correction Method for LDPC Code Combining BP and Gaussian Elimination Method", SITA 2004, 27 (1), 271-274, 2004-12-14

However, the decoding method generally requires a memory amount and a calculation amount depending on the number of rows of the check matrix × the number of columns.
In the conventional procedure, it is necessary to store all successful reception packets and calculate from the check matrix according to the result of the Gaussian elimination method. In order to increase the decoding success rate, if the number of encoded packets is increased, that is, the check matrix is increased, there is a problem that the amount of calculation and the memory used for storing and calculating the successful reception packets increase, resulting in an increase in manufacturing cost.

  The present invention has been made in order to solve the above-described problems. An encoding device and a decoding device that do not require high calculation capability and can achieve high performance while suppressing a small amount of memory. The purpose is to obtain.

  An encoding apparatus according to the present invention is an encoding apparatus that encodes an error correction code for correcting a transmission error that occurs on a transmission line. When transmitting, it includes an erasure correction encoding unit that encodes other error correction codes including some data of a certain error correction code sequence.

  Since the encoding apparatus of the present invention encodes other error correction codes including a part of data of a certain error correction code sequence, it does not require high calculation capability and has a small amount of memory. High performance can be achieved while keeping it at a minimum.

It is a block diagram which shows the communication system to which the encoding apparatus and decoding apparatus by Embodiment 1 of this invention are applied. It is explanatory drawing which shows the performance evaluation result in the number of the linked | related erasure | elimination correction code | symbol of the communication system to which the encoding apparatus and decoding apparatus by Embodiment 1 of this invention are applied. It is explanatory drawing which compares and shows the decoding procedure of the code | symbol which linked | related two packets of the communication system to which the encoding apparatus and decoding apparatus by Embodiment 1 of this invention were applied, and a double length code.

Embodiment 1 FIG.
FIG. 1 is a configuration diagram showing a communication system to which an encoding apparatus and a decoding apparatus according to Embodiment 1 of the present invention are applied.
The illustrated communication system includes a transmitter 10 and a receiver 20. The transmitter 10 includes a packet generation unit 11, an erasure correction encoding unit 12, and a transmission unit 13, and the receiver 20 includes a reception unit 21, an erasure correction decoding unit 22, and an information bit reproduction unit 23.

  In the transmitter 10, the packet generator 11 is a processor that generates a packet from information bits using a check matrix. The erasure correction encoding unit 12 performs erasure error correction encoding on the packet. That is, when the erasure correction coding unit 12 transmits an error correction code sequence encoded for each of a plurality of information sequences, the erasure correction coding unit 12 includes a part of data of a certain error correction code sequence and includes other error correction code sequences. A processing unit that performs encoding. The transmission unit 13 is a processing unit for transmitting the encoded packet to the receiver 20 via the communication path 30.

  In the receiver 20, the reception unit 21 receives a packet transmitted from the transmitter 10 via the communication path 30. The erasure correction decoding unit 22 performs error detection and erasure correction on these packets. That is, the erasure correction decoding unit 22 decodes the error correction code sequence received first, and when the decoding is successful, only the data related to other error correction codes is left and the next error correction code is decoded. If the decoding is unsuccessful, the next error-correcting code is decoded, leaving the data that is related to other error-correcting codes and has been successfully decoded, the intermediate value data of the calculation, and the information of the decoding-failed location. It is a processing unit that performs decoding in a procedure. The information bit reproduction unit 23 is a processing unit that combines the decoded packets to generate information bits.

・・・（１）
とする。丸付き数字は行番号を示す。このＨはＨ・ｖ^Ｔ＝０を満たす。以後、理解を助けるために検査行列の上に符号パケットのベクトルを記載する表現を適宜使用する。
なお、空白部分は要素０を意味し、以降同様な表現を使うものとする。 Prior to the description of the operation of the first embodiment, first, the decoding method of the erasure correction code will be described. In order to simplify the description, it is assumed that each packet is composed of 1-bit information. Actually, the processing shown below includes a plurality of bits in each packet, and the same processing is executed in parallel.
Let code word v = (u | p), u = (u ₁ u ₂ ... U _k ) be an information packet vector, and p = (p ₁ p ₂ ... P _m ) be a parity packet vector.
For example, the parity check matrix of the error correction code corresponding to v is

... (1)
And Circled numbers indicate line numbers. This H satisfies H · v ^T = 0. Hereinafter, in order to help understanding, an expression describing a vector of a code packet on a check matrix is used as appropriate.
The blank part means element 0, and hereinafter the same expression is used.

とすると、検査行列（１）用いて計算すると正しいパリティベクトルは、

となる。 The parity check matrix is a check matrix corresponding to code words of information 12 packets and parity 12 packets.
For example,

Then, the correct parity vector calculated using the check matrix (1) is

It becomes.

Now, the received packet success of 14 packets in the code word 24 packet in the receiver _{20, u 1, u 4,} u 5, u 7, u 10, u 11, u 12, p 2, p 5, p 7, p _Assuming that ₈ , p ₁₀ , p ₁₁ , and p ₁₂ , the reception success packet and the reception failure packet are first exchanged as a step of the Gaussian elimination method.
In the following example, column replacement is performed so that columns corresponding to successfully received packets are collected on the left side, and columns corresponding to unsuccessful reception, that is, lost packets are collected on the right side. In addition, the column corresponding to the packet in which the range of the square frame × mark is lost is shown.

In the calculation using the lower triangular matrix after Gaussian elimination, the increase in the calculation amount due to the increase of 1 becomes a problem. In addition, the larger the number of encoded packets, that is, the larger the parity check matrix, the greater the number of 1s included in one row, and thus the amount of calculation increases. In addition, the memory used for calculation also becomes large.
On the other hand, in the case of the same coding rate (= number of information packets / number of coded packets), the decoding success rate increases as the number of coded packets serving as a unit of coding increases.
Based on this calculation method, decoding is performed in the following procedure in actual communication.

[Decryption procedure of receiver]
It is assumed that information on the matrix H is stored in advance on the receiver 20 side.
(1) After receiving a packet, error detection of the packet is performed.
(2) In (1), if there is an error (lost packet), nothing is done.
(3) In (1), if there is no error, the reception success packet is stored. When a parity packet is received, a Gaussian elimination method is performed to check whether the number of lost packets in the information packet is equal to the rank of the matrix after the Gaussian elimination method according to the above processing.
(4) In (3), if the ranks are not equal, the next reception success packet is awaited.
(5) In (3), if the ranks are equal, storage of the reception success packet is stopped, and the lost packet is calculated using all the packets successfully received according to the matrix after the Gaussian elimination method according to the above processing.

In the case of the above decoding method, even if the calculation amount and the memory amount can be reduced, the performance is limited by the number of encoded packets in units of encoded packets. Therefore, when the performance is to be increased, the number of encoded packets is increased. However, when the number of encoded packets is increased, there is a problem that the amount of calculation and the amount of memory increase.
In order to solve this problem, a method for improving the performance without increasing the amount of memory or the calculation amount is shown below.

ｊ＝１の場合は通常の符号化を行う。
今、式（１）の検査行列の行および列がそれぞれ１／３の検査行列で定義される符号を用いるものとする。

ｊ＝２以降は以下のルールで符号化を行う。

例えば、

この操作を繰り返し、すべての符号がパリティパケットを介して関連付けられる構造とする。 [Encoding method of the present invention]

When j = 1, normal encoding is performed.
Now, it is assumed that a code defined by a 1/3 parity check matrix is used for each row and column of the parity check matrix of Equation (1).

After j = 2, encoding is performed according to the following rules.

For example,

This operation is repeated to obtain a structure in which all codes are associated through parity packets.

That is, in Embodiment 1, the erasure correction encoding unit 12 encodes other error correction codes including a part of data of a certain error correction code sequence.

例えば上記のように復号不可の場合、
ｊ＝２以上の受信の場合は、まずｊ＝ｊ−１の復号結果の中間値と関係させる受信成功したパケットのデータを用いて以下のように復号を行う。

[Decoding method of the present invention]
The receiver 20 performs normal decoding when receiving j = 1.

For example, if decryption is impossible as described above,
In the case of reception of j = 2 or more, first, decoding is performed as follows using data of a packet that has been successfully received and related to the intermediate value of the decoding result of j = j−1.

削除後の関係式は、

(1) The check matrix is deleted from the j-1th related packet and the jth successful reception packet.

The deleted relational expression is

(2) Gaussian elimination of matrix after row and column deletion of parity check matrix and lost packet recovery

(3) Replay of the j−1th related lost packet

(4) Replay of all j−1 lost packets

  That is, in the first embodiment, the erasure correction decoding unit 22 decodes the error correction code sequence received first, and when decoding is successful, only the data related to other error correction codes is left and the next When the error correction code is decoded and the decoding fails, the next error correction code is decoded with the data related to the other error correction code and the decoding success, the intermediate value data of the calculation, and the information of the decoding failure location. After that, decoding is performed in the same procedure.

  FIG. 3 shows the performance evaluation results for the number of erasure correction codes associated with FIG. CER in the figure is an abbreviation of Code Error Rate, and an encoded packet is regarded as one codeword, and indicates an error rate in units of this codeword. In the figure, the single encoded packet is (20, 10) _LDPC, which is the code of the encoded packet 20 (the number of packets including information and parity) and the information packet 10. On the other hand, if the two are associated, the encoded packet 20 and the information packet 20 use two codes, so that the total encoded packet 20 + 20 = 40 and the information packet 10 + 10 = 20. As is apparent from the two curves in the figure, it can be seen that the performance of the two encoded packets associated with each other is better than that of the single encoded packet.

FIG. 3 shows a calculation amount and a memory amount comparison between the case where the decoding procedures (1) to (4) are performed and the case where the decoding procedures (1) to (4) are not performed. This shows a comparison of the decoding procedure for a code that associates two packets with a code that is twice as long. Assuming that the decoding procedure (1) to (4) is performed as 1, if not, for example, the calculation amount of the code twice as long as A is 4 times, and the memory amount is doubled. It shows that.
As shown in FIG. 3, it can be seen that it is overwhelmingly advantageous to perform the correlated encoding using a small code, both in terms of calculation amount and memory amount.

  Thus, in Embodiment 1, the number of codeword packets can be suppressed by using a relatively small code suitable for implementation, and the amount of calculation and memory can be suppressed by reducing the check matrix. On the other hand, by having an association between small codewords, when other codewords succeed even when decoding of some codewords failed, it failed based on information of successful codewords using relevance Enable codeword playback. By suppressing the amount of calculation and the amount of memory involved in the association, it is possible to achieve high performance while using a CPU with low computing capability and suppressing the amount of memory to a small amount.

  As described above, according to the encoding apparatus of Embodiment 1, in an encoding apparatus that encodes an error correction code for correcting a transmission error that occurs on a transmission path, a plurality of information sequences are processed. Equipped with an erasure correction encoding unit that encodes other error correction codes including a part of data of a certain error correction code sequence when transmitting each encoded error correction code sequence, so it has high computing power High performance can be achieved while reducing the amount of memory required.

  In addition, according to the decoding apparatus of the first embodiment, the error correction code sequence received first is decoded. If the decoding is successful, only the data related to other error correction codes is left and the next error correction is performed. If the code is decoded and the decoding is unsuccessful, the next error-correcting code is decoded, leaving the data that is related to other error-correcting codes and has been successfully decoded, the intermediate value data of the calculation, and the information on the decoding failure location. Since the erasure correction decoding unit that performs decoding in the same procedure is provided thereafter, high performance can be achieved without requiring high calculation capability and suppressing the amount of memory to be small.

  Further, according to the decoding apparatus of the first embodiment, the erasure correction decoding unit uses the data related to another error correction code sequence of the error correction code sequence that has been successfully decoded, Since the decryption is performed again, the decryption process can be performed while not requiring a high calculation capability and suppressing the amount of memory to be small.

  Further, according to the decoding apparatus of the first embodiment, the erasure correction decoding unit succeeds in decoding a part of the data of the error correction code sequence, and when the data is related to another error correction code, the data Thus, the decoding of the other error-correcting code sequence that has failed in decoding is performed again, so that it is possible to perform the decoding process without requiring a high calculation capability and suppressing the amount of memory to a small amount.

Embodiment 2. FIG.
In Embodiment 1, the parity packet of the (j−1) th encoded packet is used as the associated data, but encoding is performed according to the following rule after j = 2. ^Let A ^j be the jth m × m permutation matrix,

となる。
なお置換行列Ａ^ｊ，ｊ≧１はｍ×ｍ以外の任意のサイズでもよく、置換行列のパターンも任意でよい。
この操作を繰り返し、すべての符号がパリティパケットを介して関連付けられる構造とする。 For example,

It becomes.
The permutation matrix A ^j , j ≧ 1 may be any size other than m × m, and the permutation matrix pattern may be arbitrary.
This operation is repeated to obtain a structure in which all codes are associated through parity packets.

In the second embodiment, a linear mapping can be realized by using an m × n matrix and converting an n-length sequence into an m-length sequence. Therefore, the process of converting a sequence using the permutation matrix A ^j is called a linear mapping. A square matrix with m = n is also included in the linear mapping.

  As described above, according to the coding apparatus of the second embodiment, the erasure correction coding unit replaces part of data of a certain error correction code sequence and then includes the data and other data. Since the error correction code is encoded, it is possible to perform the encoding process without requiring a high calculation capability and suppressing the amount of memory to be small.

  Further, according to the coding apparatus of Embodiment 2, the erasure correction coding unit performs linear mapping of a part of data of a certain error correction code sequence, and then includes other error correction codes including the data. Thus, the encoding process can be performed without requiring a high calculation capability and suppressing the amount of memory to a small amount.

例えば、

となる。
なお置換行列Ａ^ｊ，ｊ≧１はｍ×ｎ以外の任意のサイズでもよく、置換行列のパターンも任意でよい。
この操作を繰り返し、すべての符号がパリティパケットを介して関連付けられる構造とする。 Embodiment 3 FIG.
In Embodiments 1 and 2, the parity packet of the (j-1) th encoded packet is used as the data to be associated, but the entire encoded packet or any part of the packet may be used.
After j = 2, encoding is performed according to the following rules. Let A ^j be the jth m × n permutation matrix,

For example,

It becomes.
The permutation matrix A ^j , j ≧ 1 may be any size other than m × n, and the permutation matrix pattern may be arbitrary.
This operation is repeated to obtain a structure in which all codes are associated through parity packets.

例えば、

となる。
なお置換行列Ａ^ｊ，ｊ≧１はｍ×ｍ以外の任意のサイズでもよく、置換行列のパターンも任意でよい。
この操作を繰り返し、すべての符号がパリティパケットを介して関連付けられる構造とする。 Embodiment 4 FIG.
In Embodiment 1, the parity packet of the (j−1) th encoded packet is used as the associated data, but encoding is performed according to the following rule after j = 2. ^Let A ^j be the jth m × m permutation matrix,

For example,

It becomes.
The permutation matrix A ^j , j ≧ 1 may be any size other than m × m, and the permutation matrix pattern may be arbitrary.
This operation is repeated to obtain a structure in which all codes are associated through parity packets.

  As described above, according to the coding apparatus of Embodiment 4, the erasure correction coding unit transmits a parity sequence to an information sequence when transmitting an error correction code sequence coded to the information sequence. When it is necessary to lengthen the length, additional parity sequence parts are encoded, including part of the data of the error correction code sequence, so that high computing power is not required and the amount of memory is reduced. However, the encoding process can be performed.

  In addition, according to the encoding apparatus of the fourth embodiment, after replacing the partial data of the error correction code sequence, the additional parity sequence portion including the data is encoded. Therefore, the encoding process can be performed without requiring a high calculation capability and suppressing the amount of memory to a small amount.

  In addition, according to the decoding apparatus of the fourth embodiment, the first received error correction code sequence is decoded, and when the decoding is successful, only the data related to other error correction codes is left and the next parity sequence is left. If the decoding is unsuccessful and the decoding is unsuccessful, the next parity sequence is decoded, leaving the data that is related to the other parity sequence and decoding successful, the intermediate value data of the calculation, and the information of the decoding failure location, and so on. Since the erasure correction decoding unit that performs the decoding in the above procedure is provided, the decoding process can be performed without requiring a high calculation capability and suppressing the amount of memory to be small.

  In addition, according to the decoding apparatus of Embodiment 4, the erasure correction decoding unit performs other decoding failure using data related to another error correction code or parity sequence of the error correction code sequence or parity sequence that has been successfully decoded. Since the error correction code sequence or the parity sequence is decoded again, it is possible to perform the decoding process without requiring a high calculation capability and suppressing a small amount of memory.

  Further, according to the decoding apparatus of the fourth embodiment, the erasure correction decoding unit succeeds in decoding a part of the data of the error correction code sequence or the parity sequence, and the data is different from other error correction codes or the parity sequence. When related, the data is used to decode another error-correcting code sequence or parity sequence that has failed to be decoded, so decoding is not required while requiring a high calculation capacity and a small amount of memory. Processing can be performed.

となる。
なお置換行列Ａ^ｊ，ｊ≧１はｍ×ｎ以外の任意のサイズでもよく、置換行列のパターンも任意でよい。
この操作を繰り返し、すべての符号がパリティパケットを介して関連付けられる構造とする。 Embodiment 5 FIG.
In Embodiments 1 and 2, the parity packet of the (j-1) th encoded packet is used as the data to be associated, but the entire encoded packet or any part of the packet may be used.
After j = 2, encoding is performed according to the following rules. Let A ^j be the jth m × n permutation matrix,

It becomes.
The permutation matrix A ^j , j ≧ 1 may be any size other than m × n, and the permutation matrix pattern may be arbitrary.
This operation is repeated to obtain a structure in which all codes are associated through parity packets.

Embodiment 6 FIG.
In Embodiments 1 to 5, a part of the j−1th encoded packet or a related packet via the permutation matrix A ^j , j ≧ 0 is used as the associated data for the j−1th encoded packet. May be associated with encoded packets in any order.
For example, the third encoded packet may be associated with the ninth encoded packet.

となる。 Embodiment 7 FIG.
In the first to sixth embodiments, a calculation example in which the length of the packet is taken into account is shown for the sake of convenience.
For example, it is a matrix calculation that appeared frequently in the explanation so far,

It becomes.

となる。
計算機上ではバイト単位（多くの場合４バイトあるいは８バイト）で演算処理が出来る為、高速に演算処理することができる。 If you calculate 8 bits at a time,

It becomes.
Since the arithmetic processing can be performed in units of bytes (in many cases, 4 bytes or 8 bytes) on the computer, the arithmetic processing can be performed at high speed.

  Although the processing unit is expressed as a packet in the expressions so far, it can be applied to any data that is processed in a lump of bits regardless of the name of the packet, and may be called a block. is there.

  The encoding / decoding method described above can be applied to an error correction code such as a physical layer corresponding to a check matrix in bit units, in addition to an erasure correction code in which error correction is performed in packet units or block units.

  In the present invention, within the scope of the invention, any combination of the embodiments, or any modification of any component in each embodiment, or omission of any component in each embodiment is possible. .

  DESCRIPTION OF SYMBOLS 10 Transmitter, 11 Packet generation part, 12 Erasure correction encoding part, 13 Transmission part, 20 Receiver, 21 Receiving part, 22 Erasure correction decoding part, 23 Information bit reproduction | regeneration part.

Claims (11)

In an encoding device for encoding an error correction code for correcting a transmission error occurring on a transmission line,
When transmitting an error correction code sequence encoded for each of a plurality of information sequences, an erasure correction encoding unit for encoding other error correction codes including a part of data of a certain error correction code sequence is provided. An encoding apparatus comprising:   The erasure correction encoding unit performs replacement on a part of the data of the certain error correction code sequence, and then encodes the other error correction code including the data. The encoding device according to 1.   The erasure correction encoding unit performs linear mapping of a part of data of the certain error correction code sequence, and then encodes the other error correction codes including the data. Item 4. The encoding device according to Item 1.   When the erasure correction encoding unit transmits an error correction code sequence encoded with respect to the information sequence, and it is necessary to lengthen the parity sequence with respect to the information sequence, a part of the error correction code sequence The encoding apparatus according to claim 1, wherein an additional parity sequence portion is encoded including the data of the above.   5. The encoding apparatus according to claim 4, wherein after replacing a part of the data of the error correction code sequence, the additional parity sequence portion including the data is encoded. A decoding device that decodes data encoded by the encoding device according to any one of claims 1 to 3,
When the first received error correction code sequence is decoded and decoding is successful, only the data related to other error correction codes is left and the next error correction code is decoded. An erasure correction decoding unit that decodes the next error correction code by leaving the data that is related to the error correction code and successfully decoded, the intermediate value data of the calculation, and the information of the decoding failure location, and then decoding in the same procedure A decoding device comprising:   The erasure correction decoding unit re-decodes an error correction code sequence that has failed to be decoded again using data related to another error correction code sequence of the error correction code sequence that has been successfully decoded. 6. The decoding device according to 6.   The erasure correction decoding unit succeeds in decoding a part of the data of the error correction code sequence, and when the data is related to the other error correction code, the data is used to perform another error in decoding. The decoding apparatus according to claim 6, wherein the correction code sequence is decoded again. A decoding device that decodes data encoded by the encoding device according to claim 4 or 5,
The first received error correction code sequence is decoded, and when decoding is successful, only the data related to other error correction codes is left and the next parity sequence is decoded. Equipped with an erasure correction decoding unit that decodes the next parity sequence, leaving the data that is related to the parity sequence and successfully decoded, the intermediate value data of the calculation and the information of the decoding failure location, and then decoding in the same procedure A decoding device characterized by the above.   The erasure correction decoding unit decodes another error-correcting code sequence or parity sequence that has failed in decoding using the error-correcting code sequence or parity sequence that has been successfully decoded or data related to the parity sequence. 10. The decoding device according to claim 9, wherein the decoding device is performed again.   The erasure correction decoding unit succeeds in decoding a part of the data of the error correction code sequence or parity sequence, and when the data is related to the other error correction code or parity sequence, the data is used, The decoding apparatus according to claim 9, wherein the decoding of another error-correcting code sequence or parity sequence in which decoding has failed is performed again.

Images